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Optical Measurements
MSN506 notes
note: Most of the information in this presentation is collected off the web for educational purposes.
Overview
• Remember some relevant parts of EM theory
• Survey of some optical techniques– Large number of variants and different
techniques are present – It is not possible to cover all of them– Those that may be related to nanomaterial
characterization are highlighted
Why optical measurements
• Optical properties of materials can be naturally measured with optical measurements (i.e. measurements that involve light generation or scattering)
• Optical properties can be used to determine structural or other physical properties
• Generally non-destructive
Interaction of light with matter• Light is an electromagnetic wave and electric (or
magnetic fields) interact with charge• For light to interact with matter, generally
carriers must be present (which they generally are)
• Light can interact with bound or free carriers• Interaction can be non-resonant or resonant
(i.e. frequency or wavelength of light can coincide with a characteristic oscillation frequency of the sample)
The dipole moment• Emission (and absorption or scattering) of light
by the presence of a carrier is strongly affected by the dipole moment and its propertiesthe dipole moment and its properties
Oscillating dipole
Power radiated by a classical dipole
Proportional to the dipole moment
Dipole moment (Quantum Mech.)• The dipole moment can be calculated
for classical charge distributions repd =
1D potential well
Time dependent dipole during a transition between energy levels
• During a transition, dipole oscillates with a frequency
++ -
+-
EΔ=ω
Power radiated by a classical dipole
Light can be generated
Absorption can also be resonant (this can be understood via time reversal symmetry of electromagnetic waves)
A
B
A+B
A-B
Dipoles and refractive indicesDipoles and refractive indices
Refractive index as a function of frequencyis determined by the AC permitivity
Dipoles and refractive indicesDipoles and refractive indices
Refractive index as a function of frequencyis determined by the AC permitivitySometimes negative, depends on convention
Generally does not depend on frequency at optical frequencies
n2 =12
⎛⎜⎝
⎛⎝ ε' 2 + ε'' 2 ⎞
⎠ + ε' 2⎞⎟⎠
κ2 =12
⎛⎜⎝
⎛⎝ ε' 2 + ε'' 2 ⎞
⎠ – ε' 2⎞⎟⎠
n* = n + i · k
(n + ik)2 = ε' + i · ε''
Oscillator model
Classical charge oscillator
Solution(can be used to calculate polarization)
Absorbed EnergyOscillator strength
Damping factor
Lorentzian lineshape
Oscillator strength can be calculated through the transition matrix element for two given levels
Example
Silicon
Single oscillator
Density of oscillatorsStrength of oscillators
Multiple oscillators
Absorption due to an oscillatorSingle oscillator
Density of oscillators
Strength of oscillators
Absorption coefficient
Classical oscillator model is intuitive for absorption measurements
Example: Atomic spectra
Absorption lines characteristic for each atom
The Monochromator
Can be used to select a certain wavelength in a beam of white light
Diffraction grating
Blazed at an angle for higher efficiency
Multiple orders can be observed depending on the period and wavelength
Orders will repeat especially if the grating period is large
Summary of optical measurements• Thin films: absorption, reflection, transmission of
thin films, Ellisometry, refractive index models, applications, FTIR
• Atomic absorption measurements• Light scattering measurements: Raman
Scattering, Dynamic light scattering• Nonlinear property measurements• Photoluminescence• Pump/Probe experiments• Diffraction, X-ray Diffraction
Thin Films• A material is deposited (or coated) uniformly on
a substrate.• Measuring optical propeties of the film we can
learn a lot about the material• Semiconductors
• Band gap, absorption, refractive index, impurities, defects etc.
• Nanoparticles• Size distribution, crystallinity etc.
• Organic layers• Molecules
• Requires modelling of the measurement scheme
Thin film measurements
substrate
incident
reflected
absorbed
transmitted
Film of material to be characterized Support substrate of known optical properties
Incident Power = Reflected + Absorbed + Transmitted Powers
Fresnel Reflection
Normal incidence
Thin Film Reflection
TransmittanceIf the substrate is transparent to some degree in the wavelength range of interest, transmission measurements can be used to determine the optical constants. Simple formulas are available for restricted cases
1 T
Transmittance
Reflection at an angle
The Ellipsometer• Absolute quantities are always hard to measure,
and most of the time inaccurate• Making reflection measurements at two different
polarizations quickly one after another can yield better results
The Ellipsometer
Less sensitive to intensity fluctuations
The Ellipsometer
The Ellipsometer
Porosity as well
Modelling for Ellipsometry• Refractive index models (semiempirical or
empirical)• Surface and interface roughness• Composite material models, porosity• Layered materials and gradients
• A lot of complexity…• Multiple models can produce similar results
• One solution is Variable Angle Spec. Ellips.• Experience helps a lot in modelling
Refractive index models• Cauchy• Sellmeier• Other Models• Effective medium models (particularly
important for composite materials)
Example software: NKDGenGood illustration of thin film measurements
http://www.fen.bilkent.edu.tr/~aykutlu/elips.html
Example: Material Characterization using transmission data
Bulk Absorption MeasurementsExample: Atomic Absorption Spectrometer
Specialized elemental lamp for different atomsBurn the sample and analyze absorption of the flame!
Scattering Measurements• Light (generaly a laser) is incident upon
the sample• Interaction of sample and light generates
modulation of light frequency, spatial distribution and/or time
Raman Scattering
• observed by C.V. Raman 1928• Received Nobel price in 1930
Mechanical vibration excited by phonons
Electronic vibration excited by external monochromatic light
• If these are coupled by a nonlinear interaction, sum and difference frequencies of light can be generated• Light then carries information about the phonon density• Scattered light intensity is very weak compared to original
Energy Level Picture
• Selection Rules: Polariation• Raman Active modes• Requires a sharp clean light source and a high resolution monochromator
Example applications
Chemistry: Molecular vibrations
Example applications: Bulk Crystals
Different structures all at once!
300 350 400 450 5000
1
Type VII ta= 2 hours
SiOx: GeSiO 120 sccm Silicon
Inte
nsity
(a.u
)
Frequency shift (cm-1)
1000oC 900oC 800oC 700oC 600oC
1
2
5 SiGe alloy formation
Example:Low-resolution Raman Spectroscopy
• Still good for material recognition
Low resolution Raman spectrum of 1:1:1 mixture of ethanol, 2-
propanol, and 2-methyl.2-propanol.
• Surface Enhanced Raman Spec. – Plasmonic effects enhance the Raman signal– Single molecule sensitivity!
• Waveguide Raman– Multiple (large number) of interactions of laser
with sample film enhances the signal– Submonolayer sensitivity
• Micro Raman and Tip Enhanced Raman can be used for high spatial resolution
Variants
FTIR: Fourier Transform Infra Red Spectroscopy
• Interferometer has periodic resonance condition• This is used as an advantage in FTIR
FTIR principle
FTIR Operation
FTIR Operation
FTIR Operation
FTIR bands
FTIR summary• Characteristic Frequencies for certain
bonds• Dipole moment different for each bond
type, intensity varies• Density of bonds affect intensity• Frequency of vibration affected by film
stress• Overtones (harmonics) possible• … to get accurate quantitative information
meticulous analysis is needed
Dynamic Light Scattering• Theory of Operation1. A beam of monocromatic light is directed through a sample and the fluctuation of the intensity of
scattered light by the molecules is analyzed by an Avalanche Photo Diode.2. The Avalanche Photo Diode then sends electrical pulses to the Digital Signal Processor which
counts the number of photons detected in each successive time sample.3. The frequency spectrum of this signal is determined by the mathematical technique known as
autocorrelation. The similarity between the signal wave form and a slightly time delayed copy of itself is determined by multiplying the two wave forms together and then summing to give the autocorrelation function.
4. From this the Translation Diffusion Coefficient, DT can be calculated by performing a nonlinear least-squares fit of the autocorrelation coefficients to an exponential decay.
5. Under the assumption of Brownian Motion and that the molecules in solution are spheres, the Hydrodynamic Radius, RH can be calculated by using Stokes’ Equation.RH = kbT / 6πηDTkb = Boltzman’s ConstantT = Absolute Temperature in Kelvinη = Solvent Viscosity
6. Can also estimate the Molecular Weight from the RH and the sample temperature using a standard curve of Molecular Weight vs. RH of globular proteins.
7. The instruments assumes the sample fits a standard monomodal gaussian type distribution (monodisperse) and through a monomodal curve fit, determines the uniformity of the sizes of the species in solution.
8. If the sample is found to be polydisperse or nonmonomodal, the user can use the software to resolve a bimodal size distribution (bimodal analysis).
Dynamic Light Scattering
Measures size distributions of colloidal (nano) particles in a fluid medium
Dynamic Light Scattering
20 nm beads
64 nm beads
Nonlinear optical property measurements
• Z-Scan
Large spotsize means low energy density
Small spot size means large energy density
Photoluminescence• Measures radiative decay properties of
optically generated carriers
Photoluminescence
Photoluminescence• Temperature dependent• Time resolved• Resonant excitation• Pump power dependent• Polarization dependent
• By modelling carrier absorption, relaxation and emission we can estimate sample properties
Streak Camera for fast time-resolved measurements
Streak Camera
Pump-Probe experiments• Ultrafast or fast pulses are used to excite (pump) and
probe sample• Extremely fast carrier dynamics of samples can be
measured
Example setup
1 meter delay gives 3 nsec time delay
Pump-Probe experiments
X-Ray diffraction
• X-rays have extreme small wavelengths compared to visible light (angstroms)
• They can diffract off atomic planes!• X-Ray diffraction can be used to get
information about crystals, nano and micro structure of materials etc.
X-Rays• How are they produced?
High energy electrons knock out core electrons
XRD• Angle of diffraction • Width of peak gives information about
crystal domain size
XRD• Angle of diffraction tells lattice parameters • Width of peak gives information about
crystal domain size
• Molecular substances can be crystallized and analyzed by XRD